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can you give me an example of two discontinuous functions at a number a whose sum is not discontinuous at a? 
thanks!:shy:
thanks!:shy: thanks!:shy:A discontinuous function is a mathematical function that has one or more points in its domain where the function is not continuous. This means that there is a break or gap in the graph of the function at these points.
A function can be discontinuous due to several reasons, including having a removable discontinuity (the function has a hole at a certain point), a jump discontinuity (the function has a sudden change in value at a certain point), or an infinite discontinuity (the function approaches infinity or negative infinity at a certain point).
Yes, a discontinuous function can have a limit. The limit of a function at a certain point is the value that the function approaches as the input value gets closer and closer to that point. A discontinuous function can have a limit at a point where it is not continuous, as long as the limit from both sides of the point exists and is equal.
To determine if a function is continuous or discontinuous, you can graph the function and look for any breaks or gaps. Alternatively, you can evaluate the limit at each point in the domain to see if it exists and is equal to the function value at that point. If the limit does not exist or is not equal to the function value, the function is discontinuous at that point.
Some real-life examples of discontinuous functions include a light switch (the light is either on or off, there is no in-between state), a train schedule (the train arrives at a certain time, there is no continuous travel between stations), and a jump rope (the rope is either touching the ground or not, there is no gradual decrease in height).